I'm a firm believer in maintaining a portfolio that's mostly full of rock-solid stocks that you don't need to continually worry about. Having said that, however, there's nothing wrong with taking some small portion of your capital to speculate on some younger companies with tremendous growth potential.

If you have a long investment time horizon -- a minimum of five years or so -- and the stomach to withstand some growing pains along the way, here are three companies that have the potential to produce some pretty impressive growth over the long run.

A person's finger points to the top of a stock chart.

Image source: Getty Images.

1. Square

As I wrote in another article recently, Square's (SQ -0.98%) stock price has doubled in less than a year. The most recent reason for the increase was better-than-expected first-quarter earnings and a boost in the company's full-year guidance range.

Square's growth over the past few years has been absolutely remarkable. Over the past year alone, Square's payment volume has increased by 33%, revenue is up 22%, and the company is on the verge of becoming profitable, all while margin has improved.

BAr charts showing Square's growth as of Q1 2017.

Image source: Square investor presentation.

Even with the recent growth, Square's growth story could be just getting started. The company just recently expanded into the U.K., a market where small and medium-sized businesses generate over $2 trillion in revenue annually. And even with the U.K. expansion, Square is only in four countries so far. Two-thirds of businesses worldwide don't accept card payments yet, and this is expected to be a $45 trillion market by 2025. So it's fair to say that the roughly $50 billion in annual payment volume Square is currently processing leaves tons of room for opportunity.

2. BofI Holding

Online-only bank BofI Holding (AX -0.57%) has some pretty compelling competitive advantages over traditional banks. The "BofI" in its name stands for "Bank of Internet," and because the bank doesn't have to pay for physical branches and the increased staffing requirements that come with them, BofI runs a much more profitable operation than most.

In fact, BofI's non-interest expense is less than half of its peer group average, as a percentage of assets. This advantage allows the bank to generate some amazing returns: For the most recent quarter, BofI's return on equity of 21.1% and return on assets of 1.94% are well above the industry benchmarks of 10% and 1%, respectively. BofI's efficiency ratio of 27% is better than all but 4% of other banks.

Here's the best part. BofI is a relatively small bank, with $8.7 billion in assets currently. That size puts it in the same league as banks such as Florida Community Bank and South State Bank. If you haven't heard of those banks, that's kind of the point. BofI is small and is growing fast. Assets have grown by 13% over the past year, and deposits are both up by 12%.

Earnings per share have grown at a 32% annualized rate since 2011, and impressively, the bank has steadily grown its returns on equity over the years.

Bar charts showing BofI's five-year EPS and return-on-equity growth.

Image source: BofI earnings presentation.

3. Lending Club

Shares of Lending Club (LC -1.99%) have lost more than three-fourths of their market value since the company went public in early 2015, so it's understandable if you're skeptical about my claim of "jaw-dropping growth" potential here.

To be fair, the company's growth has slowed considerably, which is the primary reason for the price drop. At the time of Lending Club's IPO, the company's growth rate was phenomenal. In fact, in 2014, Lending Club originated 38% more loans than it had in its entire history before that time.

Bar chart showing Lending Club's growth through 2016's first quarter.

Image source: Lending Club Q1 2016 investor presentation.

Well, a scandal came to light not long after the IPO, and growth abruptly stopped. In fact, after the first quarter of 2016, Lending Club's originations fell by 29% and have not yet recovered.

Bar chart showing Lending Club's recent loan originations.

Image source: Lending Club.

Lending Club's management is still optimistic about the future potential, and it's worth pointing out that Lending Club's market share is less than 0.2% of the U.S. consumer debt market, so the possibility of growth is certainly there. Lending Club's management has compared the company's 2016 to Amazon.com's 2000, and if they're right, this could just be fallout from the scandal, and the company could return to growth. One thing is for sure: If Lending Club is able to successfully capture a significant market share in the U.S. consumer debt market, there could be tremendous upside for investors.